Best L∞-approximation of measurable, vector-valued functions
1984 ◽
Vol 96
(3)
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pp. 477-481
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Keyword(s):
Let (Ω, ,μ) be a probability space, and let be a sub-sigma-algebra of . Let X be a uniformly convex Banach space. Let A =L∞(Ω, , μ X) denote the Banach space of (equivalence classes of) essentially bounded μ-Bochner integrable functions g: Ω.→ X, normed by the function ∥.∥∞ defined for g ∈ A by(cf. [6] for a discussion of this space). Let B = L∞(Ω, , μ X), and let f ε A. A sufficient condition for g ε B to be a best L∞-approximation to f by elements of B is established herein.
1976 ◽
Vol 19
(1)
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pp. 7-12
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Keyword(s):
2005 ◽
Vol 72
(3)
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pp. 371-379
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1994 ◽
Vol 124
(1)
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pp. 23-31
2018 ◽
Vol 2020
(21)
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pp. 7769-7791
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2007 ◽
Vol 82
(1)
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pp. 85-109
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Keyword(s):
1998 ◽
Vol 57
(1)
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pp. 117-127
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1992 ◽
Vol 45
(1)
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pp. 25-36
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1991 ◽
Vol 14
(3)
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pp. 611-614
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2011 ◽
Vol 84
(1)
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pp. 44-48
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